Q1 Write the expression 62 8i in the standard form a bi a

Q1. Write the expression 6/(2 + 8i) in the standard form a + bi.    a. -1/5 + 4i/5    b. 3/17 + 12i/17    c. -1/5 - 4i/5    d. 3/17 - 12i/17 Q2. Choose the graph of the number line that represents x -3.    a.    b.    c.    d. Q3. Write the expression -64 and express your answer in the standard form a + bi.    a. i8    b. 8i    c. -8i    d. ±8 Q4. Evaluate (2xy + 35)/x given that x = 5 and y = 7.    a. 7    b. 49    c. 9    d. 21 Q5. The net income y (in millions of dollars) of Pet Products Unlimited from 1997 to 1999 is given by the equation y = 9x2 + 15x + 52, where x represents the number of years after 1997. Assume this trend continues and predict the year in which Pet Products Unlimited\'s net income will be $598 million.    a. 2005    b. 2004    c. 2003    d. 2006 Q6. Solve the equation x2 + 144 = 0 in the complex number system.    a. {-12, 12}    b. {12}    c. {12i}    d. {-12i, 12i} Q7. Find the real solutions of the equation 24x + 48 = x + 8.    a. {-4}    b. {6}    c. {-3}    d. {4} Q8. Solve P-5Q/3=(P+7)/2+1 for P.    a. P = (15 - 10Q)/3    b. P = (27 + 10Q)/3    c. P = (27 - 10Q)/3    d. P = (15 + 10Q)/3 Q9. Tracy can wallpaper 2 rooms in a new house in 8 hours. Together with her trainee they can wallpaper the 2 rooms in 6 hours. How long would it take the trainee working by herself to do the job?    a. 8 hr    b. 30 hr    c. 22 hr    d. 44 hr Q10. Solve x2 - 2x - 24 = 0 by using completing the square.    a. {5, -1}    b. {-6, 4}    c. {-20, -4}    d. {6, -4} Q11. Solve the inequality. Express your answer using interval notation. Graph the solution set. 7 2x + 3 15    a. (-6, -2)    b. [-6, -2]    c. [2, 6]    d. (2, 6) Q12. Multiply each side of the inequality 2 - 4x -2 by 5. What is the resulting inequality?    a. 10 - 20x -10    b. 10 - 20x -10    c. 10 - 4x -10    d. 10 - 4x -10 Q13. Translate the following sentence into a mathematical equation. Be sure to identify the meaning of all symbols. The profit derived from the sale of x video cameras is $370 per unit less the sum of $2700 costs plus $160 per unit.    a. If P is profit and x the units sold, then P = 370x - (2700 + 160x) or P = 210x - 2700.    b. If P is profit and x the units sold, then P = 370x + 2700 - 160x or P = 210x + 2700.    c. If P is profit and x the units sold, then P = 370x - (2700 - 160x) or P = 530x - 2700.    d. If P is profit and x the units sold, then P = 370/x - (2700 + 160/x) or P = 210/x - 2700. Q14. During a hurricane evacuation from the east coast of Georgia, a family traveled 210 miles west. For part of thetrip, they averaged 50 mph, but as the congestion got bad, they had to slow to 10 mph. If the total time of travel was 8 hours, how many miles did they drive at the reduced speed?    a. 57.5 mi    b. 42.5 mi    c. 52.5 mi    d. 47.5 mi Q15. Find the real solutions of the equation x + x = 56.    a. {8}    b. {49}    c. {7}    d. {64} Q16. Find the real solutions, if any, of the equation 9x2 - 32 = 12x. Use the quadratic formula.    a. {8/9, -4/9}    b. {-8/3, 4/3}    c. {8/3, -4/3}    d. {-4/9, -28/9} Q17. Solve the inequality. Express your answer using interval notation. Graph the solution set. 4x + 1 > 3x - 4    a. (-, -5]    b. (-3, )    c. [-5, )    d. (-5, ) Q18. Solve x2 - 6x - 27 = 0 by factoring.    a. {-3, 9}    b. {-3, -9}    c. {3, 9}    d. (3, -9} Q19. Solve the equation 8x2 - 3x + 1 = 0 in the complex number system.    a. {(-3/16) - (23i/16), (-3/16) + (23i/16)}    b. {(-3/16) - (23i/16), (3/16) + (23i/16)}    c. {(3/16) - (23i/16), (-3/16) + (23i/16)}    d. {(3/16) - (23i/16), (3/16) + (23i/16)} Q20. Fill in the blank with the correct inequality symbol. If x < 6, then -3x ____ -18.    a. <    b.    c.    d. > Q21. Find the real solutions of the equation (2x - 1)2 - 10(2x - 1) + 24 = 0.    a. {5/2, -3/2}    b. {-5/1, 3/2}    c. {-7/2, -5/2}    d. {7/2, 5/2} Q22. Solve the rational equation (4x-1)/(2x+3)=(6x+8)/(3x-4)    a. {28/15}    b. {-28/53}    c. {-20/53}    d. {4/3} Q23. Find the center (h, k) and radius r of the circle with the equation x2 - 16x + 64 + (y + 9)2 = 36.    a. (h, k) = (8, -9); r = 6    b. (h, k) = (9, -8); r = 36    c. (h, k) = (-9, 8); r = 6    d. (h, k) = (-8, 9); r = 36 Q24. Find the midpoint of the line segment joining the points P1 and P2. P1 = (-1, 6); P2 = (-5, 3)    a. (-6, 9)    b. (2, 3/2)    c. (4, 3)    d. (-3, 9/2) Q25. Find an equation for the line in general form Containing the points (-5, -7) and (0, 4).    a. 11x - 5y = -20    b. -2x + 4y = -16    c. -11x - 5y = -20    d. 2x - 4y = -16 Q26. Graph the following equation by plotting points: y = x3.    a.    b.    c.    d. Q27. Find an equation for the line that is parallel to the line 8x + 7y = 98 and contains the point (7, 0).    a. 8x - 7y = 56    b. 8x + 7y = 56    c. 7x + 8y = 0    d. 7x + 7y = 98 Q28. Graph the equation (x + 2)2 + (y + 3)2 = 9.    a.    b.    c.    d. Q29. Graph the follwing equation by plotting points: y = 3x + 6.    a.    b.    c.    d. Q30. List the intercepts and type(s) of symmetry, if any for y2 = -x + 9.    a. intercepts: (-9, 0), (0, 3), (0, -3); symmetric with respect to x-axis    b. intercepts: (0, -9), (3, 0), (-3, 0); symmetric with respect to y-axis    c. intercepts: (9, 0), (0, 3), (0, -3); symmetric with respect to x-axis    d. intercepts: (0, 9), (3, 0), (-3, 0); symmetric with respect to y-axis Q31. Find the slope of the line containing the points (-7, 1) and (-8, -5).    a. -1/6    b. -6    c. 1/6    d. 6 Q32. Find the slope-intercept form of the equation of the line with the properties of a horizontal line containing the point (-2, 7).    a. x = 7    b. y = 7    c. x = -2    d. y = -2 Q33. List the intercepts for the graph of the equation y = 4x.    a. (0, 0)    b. (0, 4)    c. (4, 4)    d. (4, 0) Q34. List the intercepts for the graph of the equation y = x3 - 27.    a. (0, -3), (-3, 0)    b. (0, -3), (0, 3)    c. (-27, 0), (0, 3)    d. (0, -27), (3, 0) Q35. Write 17x + 3y = 10 in slope-intercept form.    a. y = 17x/3 + 10/3    b. y = 17x - 10    c. y = 17x/3 - 10/3    d. y = -17x/3 + 10/3 Q36. Graph the line containing the point P = (-2, -8) and having slope m = 1/2.    a.    b.    c.    d. Q37. Graph the following equation by plotting points: y = 1/x.    a.    b.    c.    d. Q38. Graph the circle with radius r = 2 and center (h, k) = (-4, -1).    a.    b.    c.    d. Q39. Find the center (h, k) and radius r of the circle with the given equation (x - 6)2 + (y - 2)2 = 16.    a. (h, k) = (2, 6); r = 16    b. (h, k) = (6, 2); r = 4    c. (h, k) = (2, 6); r = 4    d. (h, k) = (6, 2); r = 16 Q40. Find the distance d(P1, P2) between the points P1 and P2. P1 = (0, -4); P2 = (5, -4)    a. 41    b. 25    c. 4    d. 5

Solution

Answer 1: a. (As explained below)

6/(2 + 8i) = 6(2 - 8i)/(2 + 8i)(2 - 8i) = (12 - 48i)/(4 + 64i²) = (12 - 48i)/(4 - 64) = (12 - 48i)/(-60) = -1/5 + 4/5i

Answer 2: d. (As explained below)

Real component is 0 and the imaginary is 3. Thus, on the number line it is x =<3. Square bracket indicates number is included and curved bracket means the number is not included. Number line at option d indicates all numbers equal to 3.

Answer 3: b. (As explained below)

-64 = - 8² = 8-1 = 8i

Answer 4: d. (As explained below)

(2xy + 35)/x = [2(5)(7) + 35] / 5 = (70 + 35) / 5 = 105 / 5 = 21

Answer 5: d. (As explained below)

y = 9x² + 15x + 52

598 = 9x² + 15x + 52

9x² + 15x + 52 - 598 = 0

9x² + 15x - 546 = 0

x = 7 suffices the above equation and hence the company\'s net income will be $598 mn in (1993 + 7) = 2006.